The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2ε with controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the ex...The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2ε with controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickhess of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11361007),supported by the National Natural Science Foundation of China(Grant Nos.7167110411601260+4 种基金11626142)the Natural Science Foundation of Guangxi Province(Grant No.2014GXNSFCA118001)the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutionsthe Project of Humanities and Social Science of Ministry of Education of China(Grant No.16YJA910003)the Fostering Project of Dominant Discipline and Talent Team of Shandong University of Finance and Economics
文摘The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2ε with controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickhess of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.
